# How to simplify the function and get the omega out of the sqrt[]?

How to simplify the function and get the omega out of the sqrt[]? I give some assumptions and hope that Mathematica can simplify the expression to the result as shown in the figure. Is there any method to solve this problem?

• Assuming[{w > 0}, w Simplify[ Sqrt[w^2 + w^4/w0^2] / w] ] gives something close. Nov 5, 2016 at 10:20
• Please, post code not pics!
– user9660
Nov 5, 2016 at 10:25

Not the form that you specified, but it does pull an ω out of the Sqrt
expr = Sqrt[ω^2 + ω^4/Subscript[ω, 0]^2]

Define a ComplexityFunction
cf = (Total[Cases[#, Power[_, n_] :> n, Infinity]^2] + LeafCount[#]) &;